Thermal Conductivity of Springs

I have a question that I've been debating with some co-workers. We are using conical springs (tapered) that most of the time in our application fully compress once engaged. We are measuring minute changes in temperature and I was wondering if a spring diffuses more heat compressed or relaxed, here are the points:

- Compressed: - This makes the spring one solid shallow cone, I believe this would increase conductivity from surface-to-surface as everything is touching, however it is somehow "tangential" (quotation marks cause it's not perfectly tangential) so the actual area for heat transfer is variable and looks like a cartoonish-caterpillar. Since we are looking for very small changes in temperature, this would increase conductivity but substantially reduce convection (since the inside of the spring is now isolated from the ambient, and the contact area with air is also reduced into this cartoonish caterpillar shape

- Relaxed: - This makes the spring as a coil, which would remind me of a heat-sink from a computer CPU, it has a lot of surface area that is in constant heat exchange with ambient due to convection, plus the coduction of the spring itself as its x-sectional area (this would be the minor heat loss)

Just wanted some opinions on this matter and which one you believe could contribute more to a change in temperature.

If you care for more details, we have an assembly of Spring touching temperature sensor touching plate to be measured, and we are recording changes of around .060 - .1°C difference when the spring is compressed vs relaxed.

The heat transfer through the metal should be very nearly the same both ways.
In the compressed state, you may get better conductance through the metal because of the metal-to-metal contact you described.
In the uncompressed state, you will get more core to air heat exchange. I don't know what the ambient air temperature is, but I would guess that is what makes the biggest difference.

I agree with Akin's law of spacecraft however I am looking for EDUCATED OPINIONS, based on heat transfer laws we've learned. If you want some more details that could help do a more educated guess. Please note I am not looking for exact numbers, I am looking if there is an obvious answer or not, maybe they're off by less than 10% difference in heat transfer.

As far as FEA analysis, I don thave that package of Solidworks and the higher ups refuse to pay 10k for it

As you can see, in theory the spring should have littler-to-no influence since there is that insulating piece of plastic between the sensor and the spring, however since we are measuring temperature to the thousand of degrees we see a difference in temperature when we compress the spring, the behavior is counter intuitive and we have a few hypotheses on what it could be.

So when do you actually see a temperature change? Do you relax the spring, then compress, relax,.. And while doing this notice a variation in temperature readings.
Perhaps some of your material displays a change in resistance in a prticular direction to heat flow under pressure, change in temperature due to stress, etc....

It appears to me from your pictures that in the compressed state, there is no effective internal air convection cooling; whereas, in the uncompressed state there is convective air cooling in and around all of the coils; and, if the heat conduction rate through the metal spring is much higher than that of the plastic base and/or the air convection cooling rate then the difference in conduction rate of contacted spring coils vs. the extended coils may not be significant. As a result, the measured temperature at the compressed condition would be higher than that of the extended spring.

I'd be surprised if convective heat transfer "dominated" this case. Natural convection is typically pretty high in thermal resistance compared to conduction, sometimes two orders of magnitude higher. If I had to guess I would say the spring once compressed flat is conducting heat more effectively because the edges of each wire touch giving a more direct path to thermal "ground."

Staff: Mentor

I'd be surprised if convective heat transfer "dominated" this case. Natural convection is typically pretty high in thermal resistance compared to conduction, sometimes two orders of magnitude higher. If I had to guess I would say the spring once compressed flat is conducting heat more effectively because the edges of each wire touch giving a more direct path to thermal "ground."

Maybe it's not as obvious as I thought. In the compressed case, one would have to consider the amount of contact surface developed between adjacent coils as a result of axial compression loading, and also the axial conduction of heat in the interstitial air in close proximity with the contact zone of the adjacent coils. I think this part can be modeled with resorting to finite element. And I think the natural convection can also be modeled, even though the successive coils are in the wake of the ones below.

A very quick analysis I made shows that a 0.016" wire spring made out of stainless steel might conduct approximately 300x as much heat flux when fully compressed to its solid length (in this analysis I assumed the contact area is around 0.001" between each wire layer). This sounds like it could be a likely candidate reason for the difference you're seeing, even if my assumptions regarding the contact area is off by a large margin.

Extended Spring Temperature Profile (8.96e-04 watts heat flux):

Compressed Spring Temperature Profile (1.38e-02 watts heat flux):

If you need a detailed analysis of your specific application but can't afford the software, I would recommend contracting with an engineering analysis subcontractor to provide the analysis you need.

That's conduction alone, I don't have time to do all the convective analysis over lunch. Convective analysis in FEA would involve a coupled CFD-thermal model.

Like I mentioned before, natural convection typically has many times higher thermal resistance than conduction. Paired with the fact that conduction's resistance also drops by potentially greater than a factor of 100 when the spring is compressed to its solid height, it seems to me conduction is the most likely driving factor.

Yeah, that might be it, I appreciate the quick analysis. The thing about this particular application and why we came up with this debate is because when you press down on it the temperature drops (counter-intuitively) you would assume the temperature should increase when you press down on it but it seems to drop about .050 C, which isnt much but its considerable in our application. Our two major possiblities for this was that the pressure on the sensor housing was somehow moving the sensor itself (the wires are in the plastic piece) so we thought some deformation of the plastic would slightly move the sensor to a higher position further away form the surface. The other theory was heat loss due to the conduction of the spring